Let $S = \{ t \in R : f(x) = |x-\pi|. (e^{|x|} - 1) \sin |x|$ is not differentiable at $t\}$. Then the set $S$ is equal to :

Question

( A ) $\{0, \pi\}$
( B ) $\{ \pi \}$
( C ) $\phi$ (an empty set)
( D ) $\{0\}$